def test_PolynomialRegression_simple():
x = np.arange(10.).reshape((10, 1))
y = np.arange(10.)
dy = 1
clf = PolynomialRegression(2).fit(x, y, dy)
y_true = clf.predict(x)
assert_allclose(y, y_true, atol=1E-10)
def test_PolynomialRegression_simple():
x = np.arange(10.).reshape((10, 1))
y = np.arange(10.)
dy = 1
clf = PolynomialRegression(2).fit(x, y, dy)
y_true = clf.predict(x)
assert_allclose(y, y_true, atol=1E-10)
def gen_vdata_poly(entry, npoly):
data = entry.Data
Rd = entry.Rdisk
Rp = entry.Vb_peak_location
z_sample = data.R
z_fit = np.array([0.5, 1, 2, 0.5 * Rd, Rd, 2 * Rd, 0.5 * Rp, Rp, 2 * Rp])
sample = data.V
error = np.sqrt(data.e_V**2 + 2**2)
V_spline = InterpolatedUnivariateSpline(z_sample, sample)
V_spline_fit = V_spline(z_fit)
n_poly = min(npoly, len(sample) - 2)
clf = PolynomialRegression(n_poly)
clf.fit(z_sample[:, None], sample, error)
y_fit = clf.predict(z_fit[:, None])
sample_fit = clf.predict(z_sample[:, None])
z_fine = np.logspace(np.log10(data.R[0]), np.log10(data.R[-1]), 100)
y_fine = clf.predict(z_fine[:, None])
pos = np.argmax(y_fine)
vmax = y_fine[pos]
rmax = z_fine[pos]
chi2_dof = (np.sum(
((sample_fit - sample) / error)**2) / (len(sample) - n_poly - 1))
dy_pred = (clf.predict(z_fit[:, None] * 1.05) -
clf.predict(z_fit[:, None] * 0.95)) / (z_fit * 0.1)
ddy_pred = (clf.predict(z_fit[:, None] * 1.05) +
clf.predict(z_fit[:, None] * 0.95) - 2 * y_fit) / (
(z_fit * 0.05)**2)
s2 = sample_fit**2 - data.Gas**2 - entry.ML_maxbulge * data.Bulge**2 - min(
entry.ML_maxdisk, 0.2) * data.Disk**2
s2 = np.array([max(item, 0.0) for item in s2])
Vdm_max = InterpolatedUnivariateSpline(z_sample, np.sqrt(s2))
s2 = sample_fit**2 - data.Gas**2 - entry.ML_maxbulge * data.Bulge**2 - min(
entry.ML_maxdisk, 0.4) * data.Disk**2
s2 = np.array([max(item, 0.0) for item in s2])
Vdm_med = InterpolatedUnivariateSpline(z_sample, np.sqrt(s2))
s2 = sample_fit**2 - data.Gas**2 - entry.ML_maxbulge * data.Bulge**2 - min(
entry.ML_maxdisk, 0.6) * data.Disk**2
s2 = np.array([max(item, 0.0) for item in s2])
Vdm_min = InterpolatedUnivariateSpline(z_sample, np.sqrt(s2))
return vmax,rmax,chi2_dof,y_fit,dy_pred,ddy_pred,sample_fit,\
Vdm_med,Vdm_max,Vdm_min,V_spline,V_spline_fit
# Generate data
z_sample, mu_sample, dmu = generate_mu_z(100, random_state=0)
cosmo = Cosmology()
z = np.linspace(0.01, 2, 1000)
mu_true = np.asarray(map(cosmo.mu, z))
#------------------------------------------------------------
# Define our classifiers
basis_mu = np.linspace(0, 2, 15)[:, None]
basis_sigma = 3 * (basis_mu[1] - basis_mu[0])
subplots = [221, 222, 223, 224]
classifiers = [
LinearRegression(),
PolynomialRegression(4),
BasisFunctionRegression('gaussian', mu=basis_mu, sigma=basis_sigma),
NadarayaWatson('gaussian', h=0.1)
]
text = [
'Straight-line Regression', '4th degree Polynomial\n Regression',
'Gaussian Basis Function\n Regression', 'Gaussian Kernel\n Regression'
]
# number of constraints of the model. Because
# Nadaraya-watson is just a weighted mean, it has only one constraint
n_constraints = [2, 5, len(basis_mu) + 1, 1]
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(8, 8))
def fit_Polynomial(features_train, labels_train, features_pred, order=3): model = PolynomialRegression(order) model.fit(features_train, labels_train) labels_pred = model.predict(features_pred) return labels_pred